Appearing in promotional material like two weathered elder statesmen of music, Lyle Lovett and John Hiatt are about to restart their on-again, off-again co-headlining tour. Though an “Acoustic Evening” date is booked for Saturday at the Akron Civic Theatre, it might as well be called “Who Knows” when it comes to the veteran artists and their set lists.

“It’s not in support of anything,” said Hiatt, calling from Boston. “It’s just going out and playing and having fun. You just never know. It just kind of depends on the mood. Lyle might play a song about a dog, and then I have to play a song about a dog, or a song about a truck running over a dog. I don’t know, it kind of goes like that. It’s very dressed down; there’s nothing show biz about it. We don’t do sets. It’s very casual. People seem to like the fact that it’s very unformed and sort of relaxed where we trade songs back and forth. It’s real. It’s like you’re sitting in a living room or something. ”

What began in the late ’80s with a tour featuring Joe Ely, Guy Clark, Lovett and Hiatt in the style of the Nashville songwriters’ circles show, where artists go around the room playing one song at a time, continues today with the latter two artists finding comfort in performing alongside each other but yet rarely together. Hiatt said on occasion they’ll share a tune, but more often than not, they play alone with a funny story or two to boot.

In looking at the two artists, their sounds and styles are mutually country-based with Lovett becoming an alt-country staple, while Hiatt has been in constant motion ranging in styles from blues and country to rock and even hints of new wave.

“I think we draw from the same sort of veins of the Southern song book, as it were, and I think we each have a sort of an odd twist to our outlook,” Hiatt said. “Not that our twists are similar, but we tend to have a particular skew on things, I think. He’s a great writer, and I really respect his material.”

Hiatt, whose latest release is 2010’s “The Open Road,” has written songs covered by a multitude of artists in a wide variety of genres including Bob Dylan, Rosanne Cash, Willie Nelson, Jewel and Bonnie Raitt, who most famously recorded “Thing Called Love.”

In talking to the music-industry veteran, a discussion about his lack of commercial success includes Sheryl Crow, who as a rising star opened for Hiatt before the release of her debut platinum album. The idea of comparing their two careers — he remains a cult act and road dog touring much of the year, while she became a mainstream rock artist — doesn’t interest Hiatt one bit. And in a nutshell, his attitude explains why he’s lasted so long.

“It’s just depends on where you want to go,” Hiatt said. “You have designs on what kind of stuff you want to write and where you want to take it. When we speak about these things, we speak in generalities. And it’s not fair. You really need more information when you talk in these general terms. And I’m not saying anything against Sheryl Crow. I think she’s talented, but my point is it’s not a competition. It’s just people making music.”